Matthew D. Blair

Visiting Assistant Professor

Address:
 Department of Mathematics
 Hylan Building
 University of Rochester
 Rochester, NY 14627

Office:
 801 Hylan Building

E-mail:
 blair ["at"] math . rochester . edu

Phone:
 585-273-2327

Research

My research area is in harmonic analysis and dispersive PDE of wave and Schroedinger type. Much of my research focuses on exploring these equations in a non-isotropic setting or on a Riemannian manifold, where the regularity of the metric and geometry of the boundary can influence how waves develop.

One important tool in my research involves phase space transforms. Phase space transforms allow one to understand waves as superpositions of "wave packets" or "coherent states", functions whose profile in space and frequency largely stays coherent under the evolution process. These methods yield estimates on solutions to dispersive PDE (Strichartz estimates) as well as eigenfunctions of the Laplacian (spectral cluster estimates).

Here are some preprints of my work:

Strichartz estimates for wave equations with coefficients of Sobolev regularity,  Communications in Partial Differential Equations, 31 (5), 2006, pp 649-688.

Spectral cluster estimates for metrics of Sobolev regularity, to appear, Transactions of the AMS.

Strichartz estimates for Schroedinger operators in compact manifolds with boundary (with H. Smith and C. Sogge), to appear, Proceedings of the AMS.

On multilinear spectral cluster estimates for manifolds with boundary (with H. Smith and C. Sogge), to appear, Mathematical Research Letters.

Teaching

Spring 2008


• Math 142, Calculus II, Webwork